Patent GB-476165-A (GB)
Title: Improvements in or relating to electrical calculating machines
IPC: G06G7/14
Filed: 1936-05-27
Abstract: 476,165. Calculating-apparatus. ELECTRICAL IMPROVEMENTS, Ltd., and BLACKBURN, C. L. May 27, 1936, No. 15023. [Class 106 (i)] An electrical calculating-machine for evaluating the product of complex quantities, which can be expressed in the form a +jb, where j is an operator representing ##-1, or the product of quaternions, which can be expressed in the form a + ib +jc + kd, where i, j and k are operators connected together by certain known relationships, comprises a group of transformers having windings which are interconnected in a number of independent circuits associated with the resolved components of the multiplicand and with the product and whose turn-ratios are associated with the resolved components of the multiplier, whilst the interconnections in the individual circuits conform to the multiplication characteristics of the system of operators, means for energizing one or more of the windings from an A.C. source in such a manner that the voltages or currents in the circuit are in phase, and means for measuring the voltages or currents in the circuits derived therefrom. The principle underlying the invention for dealing with scalar quantities is shown in Fig. 4, where six transformers are required for solving the equation d=na+mb-ca<2>. The various derived voltages and number of turns are marked in the Figure. For dealing with complex quantities, each unit of the machine contains two transformers each with three windings, as shown in Fig. 7. Each primary or basis winding is associated with a decimal switch arrangement and the two secondary or ratio windings have appropriate tappings and two pairs of terminals are connected to the basis and ratio windings. If a voltage p is applied to the upper pair of input, terminals and a voltage q to the lower pair, the voltages y and z at the upper and lower pair of output terminals will be given by the equations y = lp-mq and z = mp + lq. These expressions correspond to the real and imaginary components of the product of the complex quantities (l +jm) and (p +jq). For current transformer working the input and output terminals will be reversed. For more complicated systems the units have a number of transformers with their windings connected to conform to the characteristics of the system. As shown in Fig. 11, the connections conform to the equation Co+C1i+C2j+C3k = (Ao+ A1i+A2j+A3k) (Bo+B1i+B2j+B3k) where i, j and k are the three quaternion operators connected by the relationships i<2>=j<2>=k<2> =-1 ij=-ji= k jk = -kj = i ki =- ik = j In the multiplication of vectors there are four cases to be considered, namely, the multiplication of a scalar quantity by a vector, the multiplication of a vector by a scalar quantity, the direct or scalar multiplication of two vectors, and the skew or vector multiplication of two vectors. The scalar product of two vectors is a scalar quantity and is the product of their magnitudes multiplied by the cosine of the angle between them ; the vector product is a vector at right-angles to the two vectors having a magnitude equal to their product by the sine of the included angle. A standard unit for the different types of multiplication is shown in Fig. 15 and comprises three transformers each with three windings, and a selector switch by means of which the interconnections can be varied. The switch has four operative positions and fourteen wipers. A practical use of the invention is concerned with electrical A-C network calculations. A network as shown in Fig. 34 with non-inductive resistance and reactance can be set up in the machine with units constructed as shown in Fig. 7, and arranged as shown in Fig. 35. The turns-ratio in the transformers correspond to the real and imaginary components of the impedance R+jX of the section while the upper pair of left-hand terminals correspond to the in-phase voltage component E and the lower pair to the quadrature voltage component E<1> and the other pairs of terminals correspond to the components I and I<1> respectively. The units may be arranged to solve equations having complex roots such as a+bx+cx<2>+dx<3>=o where a, b, c, and of may be real or imaginary numbers. Other examples of the use of the apparatus are described. The machine voltages or currents may be measured directly by any suitable measuring instrument or graphically represented on the screen of a cathoderay tube as described in Specification 476,224, [Group XXXV]. Specifications 389,524 and 476,164 also are referred to.